A165449 Write the prime numbers in a string: 2357111317192329... (cf. A033308). The sequence gives the first position in the string for natural numbers.

5, 1, 2, 21, 3, 31, 4, 41, 12, 47, 5, 62, 7, 22, 77, 32, 9, 95, 11, 589, 110, 113, 1, 128, 131, 137, 63, 149, 15, 158, 8, 14, 123, 24, 2, 188, 19, 42, 72, 206, 21, 215, 23, 227, 233, 236, 25, 248, 75, 257, 78, 263, 27, 269, 275, 278, 3, 290, 29, 299, 31, 829

Offset: 1

Author

Rémy Sigrist, Sep 20 2009

Keywords

• easy
• base
• nonn

Comments

Same as A229190 but omitting the a(0) term.

Defined for all a by the normality of the Copeland-Erdős constant. - Aaron Weiner, Sep 19 2013

Examples

			The first occurrence of "111" in the string is 5, so a(111)=5.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A229190 (same sequence but including the a(0) term).

Cf. A031297.

Programs

Maple

with(StringTools): s:="": for n from 1 to 300 do s:=cat(s,convert(ithprime(n),string)): od: seq(Search(convert(n,string),s),n=1..62); # Nathaniel Johnston, May 26 2011

Mathematica

With[{prd=Flatten[IntegerDigits/@Prime[Range[1000]]],nn=10},Flatten[ Table[ SequencePosition[ prd,IntegerDigits[ n],1],{n,70}],1]][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 12 2019 *)

Python

from sympy import primerange
from itertools import count, takewhile
def afind(plimit):
  s = "".join(str(p) for p in primerange(1, plimit+1))
  return [1+s.find(str(n)) for n in takewhile(lambda i: str(i) in s, count(1))]
print(afind(10**4)) # Michael S. Branicky, May 01 2021